This talk consists of three parts:

　　Phonon transport: elastic materials experience internal resistance to the deformation caused by external forces, which is characterized by a stress-strain curve. Most theories of elastic constants are established on the linear region of the stress-strain curve. The affine elastic constants were studied in detail in the work of Born and Huang (BH). Later, its nonaffine corrections were developed by Lemaitre and Maloney (LM). Reviewing the BH theory, and comparing it with LM formalism, I will show that they address the elasticity problem from two complementary angles: LM approach works by identifying the local nonaffine forces while BH arguments are based on optimization of local nonaffine displacements. The linear regime of the stress-strain curve is also vital for elastic waves. In (elastic) disordered systems, depending on the scale of wavelength, the damping coefficient of sound waves might exhibit different behaviors. I will provide analytical results, supported by numerical evidence, of the dependence of the damping coefficient on the wavenumber, for sound waves propagating in systems having quenched disorder. The vibrational density of states of amorphous systems are also featured by these waves.

      Electron-transfer-induced heat transport (ETIHT): electron transfer is a fundamental process that drives many physical, chemical, and biological transformations. The semiclassical Marcus theory is the most common approach used for understanding such phenomena. Based on the Marcus theory, it was recently found that electron transfer between molecular sites characterized by different local temperatures is associated with heat transfer between these sites and thus contributes to heat conduction in such systems. However, Marcus theory is based on a high temperature approximation that fails at low temperatures where nuclear tunneling becomes important. I will provide, within a simple model, a unified framework that includes the deep (nuclear) tunneling limit of electron transfer and the associated heat transfer, thereby, extending the ETIHT theory to the low temperature limit.

　　Photochemical processes in the strong light-matter coupling limit: light-matter interaction in confined geometries often shows characteristic signatures such as the Purcel effect on the decay rate of molecular excitations and Rabi splitting of optical transitions. Such phenomena are analyzed for systems comprising 2-level atoms by the Tavis-Cummings model. To describe behavior of molecules in such situations an extended model is needed that includes the effect of nuclear motion. I will describe our current work to investigate the interplay between the many-molecule optical response and the local (single molecule) nuclear dynamics with possible consequences to molecular photochemistry.